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Rounding Calculator

Round any number to a chosen number of decimal places or significant figures using half up, half down, half even (banker's), ceiling, floor, truncation or away from zero, with exact decimal math.

  • Free, no sign-up
  • Runs in your browser
  • Math
Up to 100 digits; scientific notation such as 1.5e-7 is accepted. The number is handled exactly, digit by digit.
Round to
From -10 to 20. Negative values round to tens (-1), hundreds (-2) and so on.
Half modes only differ on an exact tie: half up sends 2.5 to 3 and -2.5 to -2, half down sends 2.5 to 2 and -2.5 to -3, half even picks the even neighbor.

Read the guide Rounding Methods Explained: Half Up, Banker's Rounding and More

How to use the calculator

Type or paste the number you want to round. Choose whether to round to a number of decimal places or significant figures, set how many, pick a rounding mode and press Round.

The result card shows the rounded value, how much rounding changed the number and, for significant figures, the same result in scientific notation. The details panel lists your number rounded to 0 through 6 decimal places with the same mode, which is handy when you are not sure how many places you need.

Decimal places can be negative: −1 rounds to the nearest ten, −2 to the nearest hundred, and so on.

Rounding modes

  • Half up: round to the nearest value; an exact half goes up, toward positive infinity. 2.5 becomes 3 and −2.5 becomes −2.
  • Half down: nearest value; an exact half goes down. 2.5 becomes 2 and −2.5 becomes −3.
  • Half even (banker's rounding): nearest value; an exact half goes to the even neighbor. 2.5 becomes 2 and 3.5 becomes 4.
  • Up (ceiling): always toward positive infinity. 1.21 becomes 1.3 and −1.29 becomes −1.2 at one decimal place.
  • Down (floor): always toward negative infinity.
  • Toward zero: simply cut off the extra digits, also called truncation.
  • Away from zero: always increase the size of the number, so 1.21 becomes 1.3 and −1.21 becomes −1.3.

Worked examples

Two decimal places. 2.675 with half up: the digits after the second decimal are exactly 5, a tie, so it rounds up to 2.68. Many programming languages give 2.67 here, because the computer stores 2.675 as a binary value slightly below it. This calculator works digit by digit on the number you typed, so ties are real ties.

Banker's rounding. Rounding 2.5 and 3.5 to whole numbers with half even gives 2 and 4. Over many values the ups and downs balance out, which is why it is used in finance and statistics.

Significant figures. 123456 to two significant figures is 120000, or 1.2 × 10^5 in scientific notation, and 0.0012345 to three significant figures is 0.00123.

Good to know

  • Leading zeros are not significant: 0.00123 has three significant figures.
  • With decimal places, trailing zeros are kept, so 1.5 rounded to two places shows as 1.50.
  • A whole-number result such as 120000 cannot show which zeros are significant; the scientific notation line makes that clear.
  • Up to 100 digits and exponents from −100 to 100 are accepted, which covers almost any practical number.

Frequently asked questions

Why do some programs round 1.005 to 1.00 instead of 1.01?

Most programming languages store numbers in binary, and 1.005 cannot be stored exactly; the stored value is a tiny bit below 1.005, so it rounds down. This calculator treats the number as the exact decimal you typed, so 1.005 to two places with half up gives 1.01.

What is banker's rounding?

It is another name for round half to even. A value exactly halfway between two candidates goes to the one whose last digit is even, so 0.125 becomes 0.12 and 0.135 becomes 0.14 at two decimal places. Because ties go up and down equally often, totals of many rounded values stay unbiased.

What is the difference between decimal places and significant figures?

Decimal places count digits after the decimal point, regardless of the size of the number. Significant figures count meaningful digits from the first nonzero digit, so they adapt to the number's size: 45,678 and 0.045678 both become 46,000 and 0.046 at two significant figures.

How do I round to the nearest ten, hundred or thousand?

Choose decimal places and enter a negative number: −1 for tens, −2 for hundreds, −3 for thousands. For example, 1,234.5 rounded to −2 decimal places is 1200.

Is truncating the same as rounding down?

Only for positive numbers. Truncating moves toward zero, so −2.7 becomes −2. Rounding down (floor) moves toward negative infinity, so −2.7 becomes −3.